Average Error: 14.5 → 1.2
Time: 24.3s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\left|m - n\right| - \left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right)\right) - \ell}\]
\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}
↓
e^{\left(\left|m - n\right| - \left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right)\right) - \ell}
double f(double K, double m, double n, double M, double l) {
        double r5655809 = K;
        double r5655810 = m;
        double r5655811 = n;
        double r5655812 = r5655810 + r5655811;
        double r5655813 = r5655809 * r5655812;
        double r5655814 = 2.0;
        double r5655815 = r5655813 / r5655814;
        double r5655816 = M;
        double r5655817 = r5655815 - r5655816;
        double r5655818 = cos(r5655817);
        double r5655819 = r5655812 / r5655814;
        double r5655820 = r5655819 - r5655816;
        double r5655821 = pow(r5655820, r5655814);
        double r5655822 = -r5655821;
        double r5655823 = l;
        double r5655824 = r5655810 - r5655811;
        double r5655825 = fabs(r5655824);
        double r5655826 = r5655823 - r5655825;
        double r5655827 = r5655822 - r5655826;
        double r5655828 = exp(r5655827);
        double r5655829 = r5655818 * r5655828;
        return r5655829;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r5655830 = m;
        double r5655831 = n;
        double r5655832 = r5655830 - r5655831;
        double r5655833 = fabs(r5655832);
        double r5655834 = r5655831 + r5655830;
        double r5655835 = 2.0;
        double r5655836 = r5655834 / r5655835;
        double r5655837 = M;
        double r5655838 = r5655836 - r5655837;
        double r5655839 = r5655838 * r5655838;
        double r5655840 = r5655833 - r5655839;
        double r5655841 = l;
        double r5655842 = r5655840 - r5655841;
        double r5655843 = exp(r5655842);
        return r5655843;
}

Error

Bits error versus K

Bits error versus m

Bits error versus n

Bits error versus M

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.5

    \[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]

  2. Simplified14.5

    \[\leadsto \color{blue}{e^{\left(\left|m - n\right| - \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)\right) - \ell} \cdot \cos \left(\frac{m + n}{\frac{2}{K}} - M\right)}\]

  3. Taylor expanded around 0 1.2

    \[\leadsto e^{\left(\left|m - n\right| - \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)\right) - \ell} \cdot \color{blue}{1}\]

  4. Final simplification1.2

    \[\leadsto e^{\left(\left|m - n\right| - \left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right)\right) - \ell}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))